Elevator The table of data in the spreadsheet (available on the course website and reproduced in the table below) shows the value of each state variable at different points in an elevator cycle on the Partial Derivative Machine. (Note: You may find it useful to do calculations using the spreadsheet or another computer program. If you do so, please include both a printout of your calculations and any formulas that you used in the spreadsheet.)

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Calculate the work done by each force ($F_L$ and $F_R$) during each of the four processes (loading, raising, unloading, and lowering). Discuss your method for calculating the work: do not assume a functional for for the data. Include relevant graphs of the data and give a physical explanation for the sign of each work.

What is the total energy of the system at the end of each process (loading, raising, unloading, and lowering)? Give a physical explanation for the total energy of the system after the elevator has returned to the initial state (ground floor, empty).

Calculate the following derivatives for at least two different states each (indicate the states you chose!): $\left(\frac{\partial X_R}{\partial F_R}\right)_{F_L}$ (“iso-force”) and $\left(\frac{\partial X_R}{\partial F_R}\right)_{X_L}$ (“iso-position”). Describe your method in detail and include any graphs you used.

The data you have been given was taken from real experiments done using the partial derivative machine — and some of the data wasn't perfect! Discuss how you chose to handle this during your calculations.